changing the roles of the electric and magnetic fields. Finally, eventhough the field expansions considered here use scaling functionsalone, it is straightforward to extend the idea to the case usingwavelet functions as well.

ACKNOWLEDGMENT

The authors would like to thank Dr. Thomas Witelski of the DukeUniversity Mathematics Department for his valuable input.

REFERENCES

1. M. Krumpholz and L.P.B. Katehi, MRTD: New time-domain schemesbased on multiresolution analysis, IEEE Trans Microwave TheoryTech 44 (1996), 555–571.

2. T. Dogaru and L. Carin, Multiresolution time-domain using CDFbiorthogonal wavelets, IEEE Trans Microwave Theory Tech 49(2001), 902–912.

3. I. Daubechies, Ten lectures on wavelets, SIAM (1992).4. S.G. Mallat, A wavelet tour of signal processing, Academic Press,

New York, 1998.5. A. Cohen, I. Daubechies, J.C. Feauveau, Biorthogonal bases of com-

pactly supported wavelets, Commun Pure Appl Math XLV (1992),485–560.

6. K.L. Shlager and J.B. Schneider, Comparison of the dispersion prop-erties of higher order FDTD schemes and equivalent-sized MRTDschemes, IEEE Trans Antennas Propagat 52 (2004), 1095–1104.

7. X. Wei, E. Li, and C. Liang, A new MRTD scheme based on Coifmanscaling functions for the solution of scattering problems, IEEE Micro-wave Wireless Compon Lett 12 (2002), 392–394.

8. Y.W. Cheong, Y.M. Lee, K.H. Ra, J.G. Kang, and C.C. Shin, Wavelet-Galerkin scheme of time-dependent inhomogeneous electromagneticproblems, IEEE Microwave Guided Wave Lett 9 (1999), 297–299.

9. I. Daubechies, Orthonormal bases of compactly supported wavelets II:Variations on a theme, SIAM J Math Anal 24 (1993), 499–519.

10. I. Daubechies, Orthonormal bases of compactly supported wavelets,Commun Pure Appl Math XLI (1988), 909–996.

11. K.S. Yee, Numerical solution of initial boundary value problemsinvolving Maxwell’s equations in isotropic media, IEEE Trans Anten-nas Propagat AP-14 (1966), 302–307.

© 2005 Wiley Periodicals, Inc.

LOADED FREQUENCY SELECTIVESURFACE

Qiang Gao, Dun-Bao Yan, Yun-Qi Fu, and Nai-Chang YuanMicrowave CenterSchool of Electronic Science and EngineeringNational University of Defense TechnologyChangsha, HuNan Province 410073, P. R. China

Received 31 March 2005

ABSTRACT: In this paper a new frequency-selective surface (FSS)with loadings, is introduced and analyzed using period moments meth-ods. The simulated results show that FSS may operate in different bandsand especially generate a large reduction in the resonant frequency fora fixed unit-cell size through different loadings. This provides a neworientation for FSS development. Practical circuits are fabricated, andthe measured results basically agree well with the simulated ones.© 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 47–49,2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21077

Key words: loaded frequency-selective surface; lumped element; dis-tributed element; period moment methods

1. INTRODUCTION

Frequency-selective surfaces (FSSs) have widespread applicationsover much of the electromagnetic spectra. The frequency re-sponses of FSSs highly depend on the configurations and spacingof the elements as well as on the thickness and permittivity of thedielectric layers that may be part of the screens. Figure 1 shows theequivalent-circuit models [1–3] of the FSS, which the lumpedinductances and capacitances can substitute for the periodic cell.Because the frequency responses may be altered by changing theinductances and capacitances, various FSSs can be realized byloading the distributed and lumped parameters.

2. ANALYSIS

The cells of the three FSSs are shown in Figure 2. The fieldscattered periodically from the FSS structure can be formulated byusing the periodic method of moments (PMM) [4–6]. The perti-nent equation to be solved in this paper is given by

E� tinc�r�� � E� t

scat�r�� � �0 distributed parametersZsJ� lumped parameters , (1)

where Zs � ZL�W/�L is the equivalent surface impedance of thelumped parameters ZL, loaded in the region of �W � �L.

In the MoM procedure, the subdomain bases of the rooftopfunctions and the Galerkin technique are employed to solve theunknown induced currents.

3. SIMULATION AND EXPERIMENTAL RESULTS

Three proposed resonant cells in Figure 2 are realized on substratewith �r � 3.0 and h � 0.5 mm. All the cells are closely packedon square lattices and the period P is 16 mm. Figure 3(a), 3(b), and3(c) show the transmission coefficients of Figures 2(a) and 2(b) atnormal, TE 45°, and TM 45° incidence, respectively. It is evident

Figure 1 (a) Free-standing FSS; (b) equivalent-circuit models (Xs is thecombination of lumped L and C)

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 47, No. 1, October 5 2005 47

that the higher resonance shifts towards the low frequency (7.7–6.8 GHz) and the lower resonance remains stable for the Figure2(b) shape. This is because the higher resonance is caused by theinterior loop and the loaded circular patch, which brings self-inductances and extra distributed capacitances between the interiorloop and patch, which brings self-inductances and extra distributedcapacitances between the interior loop and patch, has more effecton the interior loop than the exterior one. Figure 3(d) presents thetransmission coefficients of Figure 2(b) in different radii at normalincidence. The larger is the radius, the lower is the higher reso-nance.

Figure 4(a) shows the transmission coefficients of Figures 2(c)and 2(a) at normal incidence. Because the lumped capacitances areloaded between the exterior loops and the lower resonance basi-cally depends on the exterior loop, the lower resonance shifts

intensely and the higher one shifts slightly. Figure 4(b) shows thetransmission coefficients of Figure 2(c) with different capacitancesat normal incidence. The larger the capacitances, the lower thelower resonance is.

Waveguide simulators (WGS) [7, 8] are a convenient means ofverifying infinite-array calculations. The frequency and scan anglein a waveguide operating in the TE10 mode are related as follows:

sin � ��0

�c, (2)

where �c is the cutoff wavelength of the guide. Figure 5 shows thewaveguide simulator and the results of PMM and WGS. They arebasically in agreement.

Figure 2 Shapes of the resonant cells (units in mm): (a) double loop; (b) double loop loaded with the circular patch; (c) double loop loaded with lumpedcapacitances

Figure 3 Transmission coefficients of Figure 2(a) and 2(b): (a) normal incidence; (b) 45° TE incidence; (c) 45° TM incidence; (d) normal incidence ofthe circular patches in different radii

48 MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 47, No. 1, October 5 2005

4. CONCLUSION

This paper has described a new type of frequency-selective surface(FSS) based on distributed and lumped loadings. This FSS canchange resonance through different loadings and realize operations

in different bands. A waveguide simulator was used to confirm thetheory used for this analysis.

REFERENCES

1. B.A. Munk, Frequency-selective surface: Theory and design, Wiley,New York, 2001.

2. C. Mias, Frequency-selective absorption using lumped-element fre-quency selective surfaces, Electron Lett 39 (2003), 847–849.

3. A. Tennant and B. Chambers, A single-layer tuneable microwave ab-sorber using an active FSS, IEEE Microwave Wireless Compon Lett 14(2004), 46–47.

4. R. Mittra, C.H. Chan, and T. Cwik, Techniques for analyzing frequen-cy-selective surfaces: A review, Proc IEEE 76 (1988), 1593–1614.

5. C.-C. Chen, Transmission through a conducting screen perforated pe-riodically with apertures, IEEE Trans Microwave Theory Tech MTT-18(1979), 627–632.

6. B.J. Rubin and H.L. Bertoni, Reflection from periodically perforatedplane using a subsectional current approximation, IEEE Trans AntennasPropagat AP-31 (1983), 829–836.

7. N. Amitay, Y. Galindo, and C.-P. Wu, Theory and analysis of phasedarray antennas, Wiley–Interscience, New York, 1972.

8. H.A. Wheeler, A survey of the simulator techniques for designing aradiation element in a phased-array antenna, Proc Symp Phased ArrayAntennas Dig (1970), 157–172.

© 2005 Wiley Periodicals, Inc.

NOVEL COMPACT MICROSTRIPBANDPASS FILTER USING ATRIANGULAR RESONATOR

Jian-Xin Chen,1 Jin Shi,2 and Quan Xue1

1 Department of Electronic EngineeringCity University of Hong KongTat Chee 83, Kowloon, Hong Kong2 R&D CenterComba Telecom Systems (Guang Zhou) LTD6 Jinbi Road, Economic & Technological Development DistrictGuang Zhou, 510730, People’s Republic of China

Received 1 April 2005

ABSTRACT: A novel compact microstrip bandpass filter using a trian-gular resonator is proposed. The bandpass filter has the characteristicof the quasi-elliptical response, and several transmission zeros in thestopband are realized in order to improve the selectivity of the pass-band. A demonstration filter was designed, fabricated, and tested. Thetheoretical and experimental results are presented. © 2005 Wiley Peri-odicals, Inc. Microwave Opt Technol Lett 47: 49–50, 2005; Publishedonline in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21078

Key words: bandpass filter; elliptic-function; microstrip

1. INTRODUCTION

A conventional microstrip filter with half-wavelength open-lineresonators is too large to be used at lower microwave frequencybands. The traditional design of parallel-coupled microstrip filterssuffers from spurious response at twice the basic passband fre-quency, which causes response asymmetry in the upper and lowerstopband. Fortunately, much effort has been made to developcompact filters with suppression of spurious response. Filters usinga triangular patch [1–4] have been developed to reduce the filtersize and improve the upper-stopband selectivity. Bandpass filterswith transmission zeros have been proposed using the phase dif-

Figure 5 Waveguide simulator: (a) cross section; (b) results of the WGSand PMM

Figure 4 Transmission coefficients at normal incidence for (a) Figure2(a) and 2(c) and (b) different loaded lumped capacitances.

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS / Vol. 47, No. 1, October 5 2005 49